When the airplane flies over New York, it is an Eastern Airlines Lockheed Tri-Star (aka L-1011), when it has taxied, it is a Pan Am Boeing 707.
Near the end, after Leo hangs his scarf around his wife's neck, the camera view changes to a long shot but his scarf is no longer there. Her headscarf also changes position on her head during the scene.
Lenin's portrait hangs in a Moscow restaurant. In reality, portraits of Russian political leaders were only ever hung in official places, not in restaurants.
One of the shots of Moscow in the 1960s shows The Cathedral of Christ the Saviour. It was destroyed by Stalin in the 1930s, and rebuilt during the 1990s. In the 1960s an outdoor pool would have been in its place.